Stability of Critical Points with Interval Persistence |
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Authors: | Tamal K Dey Rephael Wenger |
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Institution: | (1) Department of Computer Science and Engineering, The Ohio State University, Columbus, OH 43210, USA |
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Abstract: | Scalar functions defined on a topological space
are at the core of many applications such as shape matching, visualization and physical simulations. Topological persistence
is an approach to characterizing these functions. It measures how long topological structures in the sub-level sets
persist as c changes. Recently it was shown that the critical values defining a topological structure with relatively large
persistence remain almost unaffected by small perturbations. This result suggests that topological persistence is a good measure
for matching and comparing scalar functions. We extend these results to critical points in the domain by redefining persistence
and critical points and replacing sub-level sets
with interval sets
. With these modifications we establish a stability result for critical points. This result is strengthened for maxima that
can be used for matching two scalar functions. |
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Keywords: | |
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